Mister Exam

Lang:

Other calculators

How to use it?
Derivative of:
Derivative of x^x^x
Derivative of x^-11
Derivative of (x+5)/(x+1)
Derivative of x^(4/3)
Identical expressions
e^ three *x*(x- one)
e cubed multiply by x multiply by (x minus 1)
e to the power of three multiply by x multiply by (x minus one)
e3*x*(x-1)
e3*x*x-1
e³*x*(x-1)
e to the power of 3*x*(x-1)
e^3x(x-1)
e3x(x-1)
e3xx-1
e^3xx-1
Similar expressions
e^3*x*(x+1)

The derivative of the function/ e^3*x*(x-1)

Derivative of e^3x(x-1)

The solution

You have entered [src]

 3          
E *x*(x - 1)

$$e^{3} x \left(x - 1\right)$$

(E^3*x)*(x - 1)

Detail solution

Apply the product rule:

$\frac{d}{d x} f{\left(x \right)} g{\left(x \right)} = f{\left(x \right)} \frac{d}{d x} g{\left(x \right)} + g{\left(x \right)} \frac{d}{d x} f{\left(x \right)}$

$f{\left(x \right)} = e^{3} x$ ; to find $\frac{d}{d x} f{\left(x \right)}$ :
1. The derivative of a constant times a function is the constant times the derivative of the function.
  1. Apply the power rule: $x$ goes to $1$
  So, the result is: $e^{3}$
$g{\left(x \right)} = x - 1$ ; to find $\frac{d}{d x} g{\left(x \right)}$ :
1. Differentiate $x - 1$ term by term:
  1. Apply the power rule: $x$ goes to $1$
  2. The derivative of the constant $-1$ is zero.
  The result is: $1$
The result is: $e^{3} x + \left(x - 1\right) e^{3}$
Now simplify:

$\left(2 x - 1\right) e^{3}$

The answer is:

$\left(2 x - 1\right) e^{3}$

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

 3              3
E *x + (x - 1)*e

$$e^{3} x + \left(x - 1\right) e^{3}$$

Simplify

The second derivative [src]

   3
2*e

$$2 e^{3}$$

Simplify

The third derivative [src]

$$0$$

Simplify